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Proof step 7 from proof btree-inv-format (previous step)

∃ height, as, alladrs. (( btree (null, null, @(n, m0, m1), height, false, ∅, nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), as, alladrs, ok) * true) )(zh) ∧ refsize-cons((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)], as) ∧ alladrs ⊆ dom nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]) ⊦ ∃ height, dirty, as, alladrs. (( btree (null, null, @(n, m0, m1), height, dirty, ∅, nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), as, alladrs, ok) * true) )(zh) ∧ refsize-cons((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)], as) ∧ alladrs ⊆ dom nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
(( btree (null, null, @(n, m0, m1), height, false, ∅, nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), as, alladrs, ok) * true) )(zh), refsize-cons((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)], as), alladrs ⊆ dom nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), as ⊆ dom nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), as ⊆ alladrs ⊦ ∃ height, dirty, as, alladrs. (( btree (null, null, @(n, m0, m1), height, dirty, ∅, nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)]), as, alladrs, ok) * true) )(zh) ∧ refsize-cons((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)], as) ∧ alladrs ⊆ dom nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)])

Rule argument

Additional information

Used simplifier rules: btree-refed-subseteq-alladrs: ⊦ (( btree(rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ alladrs;%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast;%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]